WHEEL-CARRIAGE. 
outer side of the wheel, though the centre of gra- 
vity 2 itself, from the capacity of the carriage, deriv- 
ed from its peculiar shape, is the lowest of all the 
three forms, and therefore most favourable for stabi- 
lity. But the evil in this last case arises from the 
bad shape of the axle, which is considerably bent at 
the shoulder, and brings the bottoms of the wheels 
too close; therefore the centrifugal force throws the 
centre of gravity into the vertical line p' without the 
base, and overturns the carriage as easily as that 
shown by Fg. 6. 
The proper size of the wheels is also a very im- 
portant object in a well-constructed carriage. They 
ought not to be made too high, otherwise the horse 
draws disadyantageously, nor too low, since the fric- 
tion would then be greater than necessary or expe- 
dient. Many vehicles are at the present time very 
improperly carried on remarkably small wheels, which 
causes great additional exhaustion to the horse, from 
the effects of friction, unless the roads be very smooth 
and well made. It is perhaps difficult to say what 
ought, in every case, to be the precise height of the 
wheels. It may generally be remarked, that they 
may vary between 34 and 53 feet in diameter, but 
cannot properly fall short of the one, nor exceed the 
other, without disadvantage. The fore-wheels in 
four-wheeled carriages are, in general, smaller than 
those behind, for the purpose of turning more easily, 
and giving a better position to the line of draught. 
otherwise they would be better if they were all of 
the same size. A great deal has been written on the 
relative qualities of wheels which have broad or nar- 
row felloes; and opinions are generally given in fa- 
vour of the former. The reasons assigned are, that 
the narrow wheels have a tendency to cut up and 
materially injure the roads; whereas, on the con- 
trary, the broad wheels, acting like a roller, smooth 
down, consolidate, and harden them. ‘This, as a 
general principle, is undoubtedly true; but the ques- 
tion still remains, What is the most advantageous 
breadth? It is not very easy to answer this question 
satisfactorily. By giving a considerable breadth to 
the wheels, they no doubt act as a roller, and are ad- 
vantageous to the roads; but, at the same time, they 
become heavier by the additional wood and iron, sup- 
posing the hoops nearly of the same thickness, and 
they cannot well be reduced in thickness inversely 
as their breadth, otherwise they would be too thin 
to afford proper support to the felloes, and would re- 
quire a frequent changing of the iron, which would 
be both troublesome and expensive. This would, in 
some degree, counterbalance the advantage to the 
roads, by the disadvantage of trouble, expense, and 
the additional load upon the cattle employed as a 
moving power. The difficulty appears, then, to be 
to combine the greatest advantage with the least dis- 
advantage; and this will be accomplished by making 
them neither extravagantly broad nor too narrow, 
according to the size and nature of the cart or car- 
riage, and the roads on which it will generally be 
employed. From 23 to 5 inches may be the limits 
within which they ought to be kept, except in extra- 
ordinary cases. 
We now proceed to consider the agent generally 
employed in wheel-carriages as a moving power. A 
horse, when treading in a mill-path, at the rate of 24 
miles an hour, will, on an average, raise about 150 lbs. 
by a cord hanging or passing over a pulley capable of 
easy motion, which is equivalent to 33,000 lbs. 1 
foot high in a minute. This serves as a scale to 
measure the effective exertion of a horse, and is gen- 
erally denominated a horse-power. Messrs. Boulton 
and Watt adopt a result somewhat less, or 32,000 
Ibs., in estimating the effect of their steam-engines, 
and Tredgold only 27,500. In different varieties of 
the horse, the power is doubtless different, and per- 
haps 30,000 lbs. may be a fair approximate value, in 
715 
round numbers; and, when compared with the 
strength of a man, the effect of a horse will be, in 
ordinary circumstances, nearly equivalent to that of 
five or six men. A horse generally works with ad- 
vantage about eight hours a-day only, while a man 
commonly can work, without injury, at least ten. 
The action of a horse is indeed greatly reduced by 
the length of time during which he works, though 
the rate of decrease is not perhaps well known. 
Writers on this subject have advanced different hy- 
potheses, and given formule to ascertain the effects 
under various circumstances of load and velocity, and 
some of them are at least tolerably good, by affording 
approximations somewhat useful. Thus, according 
to Euler, if f be the force which an animal exerts, 
measured by the weight with which it is actually 
loaded, in the manner just mentioned, F the utmost 
effort which the animal can exert, or the resistance 
which, at a dead pull, it is just able to overcome, 
v the velocity with which the same animal is moving 
with a given load, V the velocity with which the 
power of drawing or carrying a load entirely ceases, 
then 
offen, (Ue 32.) crpcdbicasernatad 5) 
This formula, originally proposed by Euler, from 
theoretical considerations, has been shown by M. 
Schulze to be pretty near the truth, by direct expe- 
riments. The effect of animal strength, or quantity 
of work done in a given time, will be proportional 
to f X v, or as the product of the force employed 
multiplied by the velocity of the animal’s motion. It 
is also measured by E, the effect, which will be 
E = Fv (l—<) AEA Sirsa (B) 
This, by the principles of the differential calculus, be- 
4} 
: W 
comes a maximum when v = 5, and f= > > that 
is, the effect will be greatest when the animal moves 
with one-third of the speed with which, at its great- 
est velocity it is only able to move itself, without 
carrying any load, and at the same time is loaded with 
four-ninths of the load it is capable of moving. It 
also appears that the greatest effect produced will 
be represented by the product of the two last, or 
Po al eB nt Sail (C); 
that is, multiply the greatest weight which a horse 
can move at a dead pull, by the greatest velocity with 
which he can travel without being able to move any 
weight, then ;4,ths of this product will be the great- 
est effect; or the product of the weight which he 
ought’ to exert to move a load, and the velocity at 
which he ought to travel. 
Desaguliers, one of the more early writers on this 
subject, states that a horse drawing a weight out of 
a deep well, by a rope passing over a pulley having 
little friction, will raise 200 lbs. for eight hours to- 
gether, at the rate of 24 miles an hour. Supposing 
the horse in this case to work to the greatest advan- 
tage, which is known to be nearly true, there would 
be obtained for the horse the value of F in formula 
(A), equal to 450 Ibs. V=74 miles an hour, v the 
known velocity, being 24 miles an hour. 
Hence, f=450(75--y)=8 (7.5—v)? = 2001b.(D) 
This result seems to be rather too great, when com- 
pared with some late experiments. In the eighth 
volume, new series, of the London Philosophical 
Magazine, p. 22, Mr. B. Bevan, civil engineer, has 
given the results of eight series of experiments on the 
power of horses working in the plough, which, at a 
mean for 144 horses, gives 163 lbs. for the constant 
force of each horse exerted in drawing the plough. 
If the third experiment be rejected, as it is so much 
under all the others, the mean would be 168 lbs. for 
